[Pw_forum] phonon dynamical matrix and eigenvectors
Bo Qiu
200210qb at gmail.com
Tue Apr 17 00:01:33 CEST 2012
Dear Developers and Users,
I'm new to Quantum Espresso and I want to compute phonon dynamical
matrix and eigenvectors for silicon. I can use the eigenvectors to
construct normal mode amplitudes based on independent molecular dynamics
simulated atomic velocities.
q^dot (k,\nu) =sum v_\alpha^{b,l}(t)e_\alpha^{b,*}(k,\nu)exp(-ik r_0^l)
here v is the alpha (=x,y,z) component of atomic velocity, e is the
alpha-th portion of the eigenvector of dynamical matrix D(k) and branch \nu
I tried to compare the dynamical matrix and eigenvectors for silicon at
q=(-0.333333000 -0.333333000 -0.666667000) from both Quantum Espresso
and GULP (a lattice dynamics code based on classical interatomic
potentials, chosen to be SW silicon). However, I found the dynamical
matrices do not agree. The eigenvectors are also completely different.
As a result, if I use the eigenvector e*(k,\nu) from GULP to construct
q^dot, its Fourier transform shows single peak at the corresponding
phonon mode frequency, which is expected for single mode (k,\nu).
However, if I use the eigenvector e'*(k,\nu) from QE, the FT shows
multiple peaks, with peak positions corresponding to frequencies of
multiple branches (\nu, \nu', \nu'', etc), which is incorrect.
I first thought maybe there is some discrepancy in the definition of
coordinate systems so e'*(k,\nu) from QE may be linear combinations of
e*(k,\nu) from GULP. However I made sure the primitive cell vectors for
both computation is
cubic
0.000000000 0.500000000 0.500000000
0.500000000 0.000000000 0.500000000
0.500000000 0.500000000 0.000000000
and the internal coordinates for both are:
1 1 0.0000000 0.0000000 0.0000000
2 1 0.2500000 0.2500000 0.2500000
I suppose when the dynamical matrices are defined under the same
coordinate systems and they should be very similar (despite inaccuracy
of classical SW potential), so should the corresponding eigenvectors. I
don't quite understand what went wrong or if there is some hidden
transformation to the dynamical matrix/ eigenvectors in QE. Could you
please help me with that? Sorry for the lengthy email!
===========================
QE:
dynamical matrix:
1 1
0.26584460 0.00000000 0.01095706 0.00000000 0.01178255
0.00797619
0.01095706 0.00000000 0.26584460 0.00000000 0.01178255
0.00797619
0.01178255 -0.00797619 0.01178255 -0.00797619 0.29527850
0.00000000
1 2
0.10051503 -0.05636929 -0.11838412 -0.03489786 -0.07026611
0.03761305
-0.11838412 -0.03489786 0.10051503 -0.05636929 -0.07026611
0.03761305
-0.07026611 0.03761305 -0.07026611 0.03761305 0.11544724
-0.05301088
2 1
0.10051503 0.05636929 -0.11838412 0.03489786 -0.07026611
-0.03761305
-0.11838412 0.03489786 0.10051503 0.05636929 -0.07026611
-0.03761305
-0.07026611 -0.03761305 -0.07026611 -0.03761305 0.11544724
0.05301088
2 2
0.26584460 0.00000000 0.01095706 0.00000000 0.01178255
-0.00797619
0.01095706 0.00000000 0.26584460 0.00000000 0.01178255
-0.00797619
0.01178255 0.00797619 0.01178255 0.00797619 0.29527850
0.00000000
GULP:
dynamical matrix:
Real Dynamical matrix :
0.612757 0.007542 0.000000 -0.162617 0.306835 0.000000
0.007542 0.612757 0.000000 0.306835 -0.162617 0.000000
0.000000 0.000000 0.650468 0.000000 0.000000 -0.162617
-0.162617 0.306835 0.000000 0.612757 0.007542 0.000000
0.306835 -0.162617 0.000000 0.007542 0.612757 0.000000
0.000000 0.000000 -0.162617 0.000000 0.000000 0.650468
Imaginary Dynamical matrix :
0.000000 0.000000 -0.026128 0.000001 0.000000 0.177151
0.000000 0.000000 -0.026128 0.000000 0.000001 0.177151
0.026128 0.026128 0.000000 0.177151 0.177151 0.000001
-0.000001 0.000000 -0.177151 0.000000 0.000000 0.026128
0.000000 -0.000001 -0.177151 0.000000 0.000000 0.026128
-0.177151 -0.177151 -0.000001 -0.026128 -0.026128 0.000000
====================================
The corresponding eigenvectors:
QE:
omega( 1) = 3.843790 [THz] = 128.215027 [cm-1]
( -0.466622 0.179622 0.466622 -0.179622 0.000000 0.000000 )
( 0.481928 -0.133213 -0.481928 0.133213 0.000000 0.000000 )
omega( 2) = 5.191233 [THz] = 173.160893 [cm-1]
( 0.240380 -0.225674 0.240380 -0.225674 -0.500138 0.180108 )
( -0.302624 -0.130882 -0.302624 -0.130882 0.531580 0.000000 )
omega( 3) = 9.773114 [THz] = 325.995997 [cm-1]
( -0.301588 -0.275885 -0.301588 -0.275885 -0.088915 -0.397439 )
( -0.335073 -0.234081 -0.335073 -0.234081 -0.407264 0.000000 )
omega( 4) = 12.316327 [THz] = 410.828451 [cm-1]
( -0.266508 -0.236976 -0.266508 -0.236976 -0.152029 -0.471719 )
( 0.307303 0.180967 0.307303 0.180967 0.495612 0.000000 )
omega( 5) = 14.170455 [THz] = 472.675510 [cm-1]
( -0.445864 0.226286 0.445864 -0.226286 0.000000 0.000000 )
( -0.465825 0.181680 0.465825 -0.181680 0.000000 0.000000 )
omega( 6) = 14.480825 [THz] = 483.028344 [cm-1]
( 0.214285 -0.226094 0.214285 -0.226094 -0.551429 0.043056 )
( 0.231234 0.208727 0.231234 0.208727 -0.553107 0.000000 )
GULP:
Frequency 192.1405 270.1120
368.8443
Real Imaginary Real Imaginary
Real Imaginary
1 x -0.473100 -0.161793 0.000000 0.358390 0.000002 0.368133
1 y 0.473100 0.161793 0.000000 0.358390 0.000002 0.368133
1 z 0.000000 0.000000 0.493066 0.000003 -0.478494 -0.000001
2 x -0.473100 -0.161792 0.000002 -0.358390 -0.000002 0.368133
2 y 0.473100 0.161792 0.000002 -0.358390 -0.000002 0.368133
2 z 0.000000 0.000000 0.493066 0.000000 0.478494 0.000000
Frequency 434.9274 540.5867
541.2499
Real Imaginary Real Imaginary
Real Imaginary
1 x -0.000002 -0.348650 -0.018584 -0.499655 0.000000 0.338346
1 y -0.000002 -0.348650 0.018584 0.499655 0.000000 0.338346
1 z 0.506840 0.000000 0.000000 0.000000 0.520618 0.000001
2 x -0.000001 0.348650 0.018585 0.499654 -0.000001 0.338346
2 y -0.000001 0.348650 -0.018585 -0.499654 -0.000001 0.338346
2 z 0.506840 0.000000 0.000000 0.000000 -0.520618 0.000000
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